Application of the Haar wavelet-based discretization technique to problems of orthotropic plates and shells

The Haar wavelet discretization technique for solving the elastic bending problems of orthotropic plates and shells is proposed. Free transverse vibrations of orthotropic rectangular plates with a variable thickness in one direction are considered as a model problem. In the case of constant plate thickness, the numerical results are validated by comparing them with an exact solution. The results obtained are found to be in good agreement with those available in the literature.     

Optimal material orientation of linear and non-linear elastic 3D anisotropic materials

Optimal material orientation problems of linear and non-linear elastic three-dimensional anisotropic materials are studied. Most commonly, the energy based formulation is applied for solving orientational design problems of anisotropic materials, considering elastic energy density as a measure of the stress strain state. The same approach is used in the current study, but the strength criteria based approaches are also discussed. A simple relation between the stationary conditions in terms of Euler angles and the optimality conditions in terms of strains is pointed out. The complexity analysis of the different existing optimality conditions has been performed. The solution of the posed optimization problem is decomposed into the strain level solution, search for global extremes and evaluation of Euler angles (parameters). The results obtained are extended to some nonlinear elastic material models.     

Orientational Design of Nonorthotropic Two-Dimensional Materials

A linear elastic nonorthotropic two-dimensional material with six independent elastic parameters is considered. Different criteria for comparison of constitutive matrices, which may be mutually rotated, are discussed. Optimal material orientations of a nonorthotropic material, which correspond to extreme values of the energy density, are determined. The results obtained are extended to some nonlinear elastic material models.     

Chemical and Biological Characteristics of Oxytropis pseudoglandulosa Plant of Mongolian Origin

Oxytropis pseudoglandulosa is used in Mongolian traditional medicine due to its numerous reported health-promoting effects. To date, there are very few scientific reports that describe this species. In this article, its volatile oil composition, lipid extract composition, total phenolic and flavonoid content, antibacterial and allergenic properties are elucidated for the first time. Hexadecanoic acid, fokienol and tricosane were determined as the most notable components of the volatile oil, at 13.13, 11.46 and 5.55%, respectively. Methyl benzoate was shown to be the most abundant component of lipid extract at 40.69, followed by (E)-prop-2-enoic acid, 3-phenyl- and benzenepropanoic acid, at 18.55 and 9.97%. With a TPC of 6.620 mg GAE g⁻¹ and TFC of 10.316 mg QE g⁻¹, the plant extract of O. pseudoglandulosa indicated good antioxidant activity measured by IC₅₀ at 18.761 µg mL⁻¹. Of the 12 tested microorganisms, B. subtilis and S. cerevisiae were the shown to be most susceptible to the plant extract, with MIC at 2.081 and 0.260% (v/v), respectively. Bet v 1—a major birch pollen allergen found in plant-based foods—was determined to be at 192.02 ng g⁻¹ with ELISA. Such a wide spectrum of biological activity indicated by O. pseudoglandulosa lends credence for its application in food industry. Its exerted antioxidant and antimicrobial effects could improve preservation of low-processed food dedicated for consumers afflicted with allergies. Hexadecanoic acid supplemented in foods with dietary plant extracts could add to the potential anti-inflammatory impact. The analysis of lipid makeup suggests O. pseudoglandulosa extract could also be considered as natural pesticide in organic farming.     

Modelling a new composite from a recycled GFRP

The mechanical reprocessing of different types of plastic scrap in high-energy disintegrator mills in direct and selective milling systems is considered. The grindabilty and separation of components of composites-an acrylic plastic and glass fibers-are analyzed. The relation between the density of the filler material and the fractions of a polymethylmethacrylate powder is modelled on the basis of experimental data. Artificial neural networks and a hybrid genetic algorithm are used to design a new composite from a recycled glass-fiber-reinforced plastic. Russian translation in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 6, pp. 881–894, November–December, 2008.     

Nonlinear constitutive behavior of orthotropic materials

The problem of optimal material orientation is studied in the case of nonlinear elastic materials. Optimal orientations corresponding to extreme (maximal or minimal) energy density are obtained for orthotropic materials. The material behavior (the stress-strain relation) is simulated in a general form, which includes, as particular cases, different versions of the power law stress-strain relations. The optimality conditions are derived for the general cases. Local and global extremums are determined for particular cases.Presented at the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000).Tartu University, Estonia. Published in Mekhanika Kompozitnykh Materialov, Vol. 36, No. 4, pp. 445–454, March–April, 2000.     

Static Response and Buckling Loads of Multilayered Composite Beams Using the Refined Zigzag Theory and Higher-Order Haar Wavelet Method

Mechanics of Composite Materials - The paper presents a review of Haar wavelet methods and an application of the higher-order Haar wavelet method to study the behavior of multilayered composite...     

Orientational Design of Anisotropic Materials Using the Hill and Tsai–Wu Strength Criteria

Linearly elastic two- and three-dimensional orthotropic materials are considered. The problems of optimal material orientation are studied in the cases of the Hill and Tsai–Wu strength criteria. The necessary optimality conditions are derived for a 3D orthotropic material. In the case of a 2D orthotropic material, an analytical solution is obtained. An analysis of global and local extrema is presented.     

Optimal design of axisymmetric plastic shallow shells of von Mises material

An optimal design technique developed earlier for axisymmetric plates and circular cylindrical shells is accommodated for shallow spherical shells subjected to uniform transverse pressure. Material of the shells is assumed to be rigid-plastic obeying the von Mises yield condition and the associated deformation law. The post-yield behaviour of the shells is taken into account. The weight minimization is performed under the condition that the maximal deflection of the shell of variable thickness coincides with the deflection of the reference shell of constant thickness. The problem is transformed into a non-linear boundary value problem which is solved numerically.     

Weak formulation based Haar wavelet method for solving differential equations

The Haar wavelet based discretization method for solving differential equations is developed. Nonlinear Burgers equation is considered as a test problem. Both, strong and weak formulations based approaches are discussed. The discretization scheme proposed is based on the weak formulation. An attempt is made to combine the advantages of the FEM and Haar wavelets. The obtained numerical results have been validated against a closed form analytical solution as well as FEM results. Good agreement with the exact solution has been observed.